A function is a reletion with one output for each input. Then, in a ordered pair inputs and outputs represent a relationship between two values.
Some relationships make sence (one output for each input) and others dont't.
Functions are relationsips that make sence.
All functions are relations, but not all relations are functionsWhat coordinates point can I plot in the graph? It can't be a decimals point, It has to be whole numbers because the graph doesn't let me put for example 4.86 or a fraction
First, we can start input small whole numbers in the function to see if we get a whole number. Let's try with 0, 1 and 2:
[tex]\begin{gathered} y=(\frac{1}{2})^{0+1}-9=\frac{1}{2}-9=-8.5 \\ . \\ y=(\frac{1}{2})^{1+1}-9=\frac{1}{4}-9=-8.75 \\ . \\ y=(\frac{1}{2})^{2+1}-9=\frac{1}{8}-9=-8.875 \end{gathered}[/tex]None of those values worked. Let's try negative integers, such as -1 and -2:
[tex]\begin{gathered} y=(\frac{1}{2})^{-1+1}-9=(\frac{1}{2})^0-9=1-9=-8 \\ . \\ y=(\frac{1}{2})^{-2+1}-9=(\frac{1}{2})^{-1}-9=2-9=-7 \end{gathered}[/tex]We get integer coordinates if we use negative integers. Then, we need at least 5 points. Let's use x = -1, -2, -3, -4, -5
[tex]\begin{gathered} y=(\frac{1}{2})^{-3+1}-9=(\frac{1}{2})^{-2}-9=2^2-9=4-9=-5 \\ . \\ y=(\frac{1}{2})^{-4+1}-9=(\frac{1}{2})^{-3}-9=2^3-9=8-9=-1 \\ . \\ y=(\frac{1}{2})^{-5+1}-9=(\frac{1}{2})^{-4}-9=2^4-9=16-9=7 \end{gathered}[/tex]We have the points:
(-1, -8), (-2, -7), (-3, -5), (-4, -1) and (-5, 7)
If we locate them in the cartesian plane:
And now, we can estimate the graph. An exponential function where the base is smaller than 1, describes an exponential decay, and the term "-9" is applying a shift 9 units down, and also y = -9 is a horizontal asymptote. With all this and the points we just found:
nancy had 209 dollars to spend on 6 of the most mundane books.after buying them she had 17 dollars. on average, how much did each book cost
The average cost of each book that Nancy got is $32
What is cost?Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice
In the question, the commodity is mundane books
How to solve how much each book costgiven that
Nancy had 209 dollars to spend
number of books = 6
amount remaining after buying = $17
The question can be represented mathematically as
6x + 17 = 209
where x is the cost of the each book
6x + 17 = 209
6x = 209 - 17
6x = 192
dividing through by 6
6x / 6 = 192 / 6
x = 32
hence each book costs $32
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∠A and \angle B∠B are complementary angles. If \text{m}\angle A=(6x+2)^{\circ}m∠A=(6x+2)
∘
and \text{m}\angle B=(4x+18)^{\circ}m∠B=(4x+18)
∘
, then find the measure of \angle A∠A.
The measure of ∠ A is 44 degrees.
Given that:-
∠ A and ∠ B are complementary angles.
∠ A = (6x +2) degrees
∠ B = (4x + 18) degrees
We have to find the measure of ∠ A.
We know that the sum of two complementary angles is 90 degrees.
Hence, we can write,
(6x + 2) + (4x + 18) = 90
(6x + 4x) + (2 + 18) = 90
10x + 20 = 90
10x = 90 - 20
10x = 70
x = 70/10
x = 7 degrees
Hence,
∠ A = 6*7 + 2 = 42 +2 = 44 degrees.
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Can someone help me i will give brainlest :) 12, 13, 14, only do those one's
Plotted Answers:
12.) See attached for my work
13.) See attached for my work
14.) See attached for my work
Simplified Answers:
12.) y > –24
13.) x ≥ –12
14.) x > –7
Hope that helps! Have an amazing rest of your day! Please consider giving me the Brainliest! :)
Question 7 013 points Redo Which theorem is depicted by the figure and information shown below? R S Theorem? ZRAZT 2Qazs A) Opposite sides of parallelograms are congruent (Tm 16-A) B) Opposte angles in a parallelogram are congruent. (Tm 16-B) C) The sum of any consecutive angles within a parallelogram equals 180 (Tm 16-C) D) The diagonals of a parallelogram bisect each other (Tm 16-D) E) The diagonal of a parallelogram separates it into two congruent triangles (Tm 16-E)
Answer:
B. Opposite angles in a parallelogram are congruent.
Explanation:
The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.
Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.
So, the answer is B. Opposite angles in a parallelogram are congruent.
The latest crime statistics in the united states suggest that eighteen-to-twenty-four-year-olds make up about – percent of the population but account for – percent of criminal arrests, while people sixty-five and older make up more than – percent of the population but account for less than – percent of arrests
Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.
The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic requires division into further sub-categories. One common way to do this is by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.
Hence, percentage of people whose age is in between 18-24 is 7%,
people from age 18-24 engaged in illegal work=15%,
percentage of people whose age is 65 or more than =13%,
people involved in crime having age more than or equal to 65=1%
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Use the factor theorem to find all real zeros and one factor.
f(x) = 2x³-9x² + 13x - 6; x - 1
Answer:
x = {1, 1.5, 2}Step-by-step explanation:
GivenPolynomial f(x) = 2x³ - 9x² + 13x - 6, One of the factors x - 1.Factorize the polynomial using the given details.
Since one of the factors known, try to factor it out and futher:
2x³ - 9x² + 13x - 6 = 2x³ - 2x² - 7x² + 7x + 6x - 6 = 2x²(x - 1) - 7x(x - 1) + 6(x - 1) = (x - 1)(2x² - 7x + 6) = (x - 1)(2x² - 3x - 4x + 6) = (x - 1)[x(2x - 3) - 2(2x - 3)] =(x - 1)(x - 2)(2x - 3)Find its zero's:
x - 1 = 0 or x - 2 = 0 or 2x - 3 = 0x = 1 or x = 2 or x = 1.5Answer:
[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]
Step-by-step explanation:
Factor Theorem
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.
Given polynomial function:
[tex]f(x)=2x^3-9x^2+13x-6[/tex]
Sum the coefficients:
[tex]\implies 2-9+13-6=0[/tex]
As the sum of the coefficients is zero, (x - 1) is a factor.
Therefore:
[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]
Expand the brackets:
[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]
[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]
Compare the coefficients with the given polynomial.
As the coefficient of the leading term of the polynomial is 2:
[tex]\implies a=2[/tex]
As the coefficient of the term in x² is -9:
[tex]\implies b-a=-9[/tex]
[tex]\implies b-2=-9[/tex]
[tex]\implies b=-7[/tex]
As the constant of the given polynomial is -6:
[tex]\implies c=6[/tex]
Substitute the found values of a, b and c into the factored form of the polynomial:
[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]
Factor the quadratic:
[tex]\implies 2x^2-7x+6[/tex]
[tex]\implies 2x^2-4x-3x+6[/tex]
[tex]\implies 2x(x-2)-3(x-2)[/tex]
[tex]\implies (2x-3)(x-2)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]
To find the zeros, set the function to zero:
[tex]\implies f(x)=0[/tex]
[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]
Apply the zero-product property:
[tex]\implies x-1=0 \implies x=1[/tex]
[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]
[tex]\implies x-2=0 \implies x=2[/tex]
Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.
A construction crew has just built a new road. They built the road at a rate of 18.75 kilometers per week. They worked for 3 weeks. How many kilometers of road did they build?
Answer:
6.25 weeks
Step-by-step explanation:
Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.
what are the coordinates of the image P for a dilation with center (0,0) and a scale factor 2? answer choices :• (2,0) • (0,6)• (-4, 2)• (0,5)
Rule for a dilation with center (0,0)
[tex](x,y)\rightarrow(kx,ky)[/tex]k is the scale factor.
For point P (0,3):
[tex]\begin{gathered} P(0,3)\rightarrow P^{\prime}(2(0),2(3)) \\ P(0,3)\rightarrow P^{\prime}(0,6) \end{gathered}[/tex]Then the coordiantes of point P after the dilation are (0,6)how many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
The number of ways to plan her schedule of menus for the 20 school days is 10^20.
How to many number of ways to plan her schedule?To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.
For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.
The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.
How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?
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Natalia and her friends held a bake sale to benefit a local charity. The friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale. They collected $60 on the first day and $88 on the second day. Write an equation to represent the amount R Natalia and her friends raised after selling c cakes.
In linear equation, R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. A linear equation in one variable would be 9x + 78 = 18, for instance.The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .
Where,
y = R (amount of cake sold in dollars)
x = c (cakes sold)
m = slope
b = y-intercept.
The equation would look like
R = mc + b
We need to find the value of m and b, to get an equation to represent the situation.
The first point we have from the information given is (15, 60) => 15 cakes sold for $60.
The second point is (22, 88) => 22 cakes sold for $88.
Slope(m) = 88 - 60/22 - 15 = 28/7 = 4
To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b
60 = 4(15) + b
60 = 60 + b
b = 0
Since b = 0, this means there is a proportional relationship between R and c.
Substitute m = 4 and b = 0 into R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.
R = 4c + 0
R = 4c
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For f(x) = 2x + 1 and g(x) = 2
7, find (f- g)(x)
The value of (f- g)(x) is 2x - 26.
This is a question of subtraction of functions.
Subtraction of functions
The subtraction of function involves the creation of a new function through the addition of two other functions.
Subtraction of one real-valued function from another.
Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.
Given that:-
f(x) = 2x + 1
g(x) = 27
We have to find the value of (f- g)(x)
We know that,
(f- g)(x) = f(x) - g(x)
Hence, we can write,
(f- g)(x) = 2x + 1 - 27 = 2x - 26
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Identify the following scatter plots as having a positive correlation,
negative correlation, or no correlation. Explain your reasoning.
Need help ASAP!!!
The given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.
What is correlation?Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.
Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.
Negative correlation is when two variables move in different directions. When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative correlation is always negative.
Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.
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Which one is it because i thought it was 32g+26
The equivalent expression of 4(8g + 5) + 6 is 4(5 + 8g) + 6
How to find equivalent expression?Equivalent expressions are expressions that work the same even though they look different.
In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Therefore, let's find the equivalent expression of 4(8g + 5) + 6.
Hence,
4(8g + 5) + 6
32g + 20 + 6
32g + 26
Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6
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Marty invested $7000 in treasury notes and stocks. The stocks paid 7% in the notes paid 8%, giving an annual income of $535. How much is invested into the treasury notes?
Answer:
3500
Step-by-step explanation:
split 7000 in half for stocks and treasury= 3500 each.
7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.
x + 3y = 1 ; 7x + 8y = 11 solve by substitution.
Step-by-step explanation:
x + 3y = 1
x = 1 - 3y-(i)
7x + 8y = 11
x= 11-8y/7-(ii)
substituting eqn (i) in eqn (ii)
11-8y/7= 1-3y
11-8y=7-21y
13y=-4
y=-4/13
putting the value of y in eqn (i)
x=1-(-12/13)
x=25/13
For the rhombus below, find the measures
Select the two values of x that are roots of this equation.3x² + 1 = 5xA. x =5+√13x = 5+√136☐ B. x =5-√136□ C. x=-1-√59X6D. X =-1+√596
3x^2 + 1 = 5x
3x^2 - 5x + 1 = 0
quadratic formula
[tex]x=-\frac{b\pm\sqrt{b^2-4ac}}{2a}[/tex]where ax^2 + bx + c = 0
so
[tex]x=\frac{5\pm\sqrt{-5^2-4(3)(1)}}{2(3)}[/tex][tex]x=\frac{5\pm\sqrt{25-12}}{6}[/tex]You can see that the 25 - 12 = 13 so the answers are A and B
a grocery store wonders if their sales will be better if they play ambient music or no music at all. each day for 222 months, the manager flips a coin to determine whether or not the store will play music that day. at the end of the 222 months, the manager finds that, on average, sales were significantly better on days where music was playing. what conclusion can they draw from this study?
Answer:
They should play music
Step-by-step explanation:
They should play music obviously because the sales were higher
simplify 20:15
simplify 35:49
simplify 81:36
simplify 27:45
simplify 21:36
pls help me i’m crying rn bro
Answer:
1. 4:3
2. 5:7
3. 9:4
4. 3:5
5. 7:12
Step-by-step explanation:
I'm sure you don't care how to get the answers, you just want them :)
Please help *100 POINTS*
New Orleans is 2 feet under seas level.
Salton City has a elevation lower than New Orleans.
What is a possible elevation, in feet of Salton City
With explanation please
The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.
What is a number line?A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.
The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level
The elevation of Salton City = Lower than the elevation of New Orleans
Required; The possible elevation of Salton City
The elevation of Salton City can be found by presenting the given information on a number line as follows;
Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;
<___|-3______|-2____|0______>
' S. N. SL
A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet
The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet
-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level
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Use the given endpoint R and midpoint M of RS¯ to find the coordinates of the other endpoint S.
R(3, 0), M(0, 5)
Step-by-step explanation:
the midpoint coordinates between 2 points A and B are
((xa + xb)/2, (ya + yb)/2)
xa = 3
ya = 0
and so we get
(3 + xb)/2 = 0
3 + xb = 0
xb = -3
(0 + yb)/2 = 5
yb = 10
therefore, S = (-3, 10)
11th term of the arithmetic sequence with the rule an= - 2 + 6(n - 1)?
⇒Given that the general rule to find the nth term is
[tex]T_{n} =-2+6(n-1)[/tex]
⇒To find the 11th term this means that they need a term which is in the position 11
⇒To get the number we plug in the 11 which is the position in the place of n and simplify.
[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]
The 11th term is 58
Goodluck!!!
reid took seven tests. on the first five tests that he took, he averaged $86$ points. on the last three tests, he averaged $95$ points. if he averaged $88$ points on all seven tests, how many points did he average on the last two tests?
The points that he average on the last two tests will be 93 points.
What is mean?A mean is the average of the set of numbers that are given.
On the first five tests that he took, he averaged 86 points. The total points will be:
= 86 × 5
= 430 points
He averaged 88 points on all seven tests. The total will be:
= (88 × 7)
= 616 points
The point average on the last two tests will be:
= (616 - 430)/2
= 186/2
= 93 points
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PLEASE HELP ASAP!!!!!!!!!!!!! WITH STEPS PLEASEEEEEE!!!!!!!!!!!!!
Given f(x) = x2 + 4x − 1, describe the new function g(x) = f(x + 4)
Step-by-step explanation:
This should be the right solution.
Write the quadratic equation that has roots -1-rt2/3 and -1+rt2/3 if its coefficient with x^2 is equal to 1
[tex]\frac{-1-\sqrt{2}}{3}[/tex] [tex]\frac{-1+\sqrt{2} }{3}[/tex]
The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9
How to determine the quadratic equation?From the question, the given parameters are:
Roots = (-1 - √2)/3 and (-1 + √2)/3
The quadratic equation is then calculated as
f(x) = The products of (x - roots)
Substitute the known values in the above equation
So, we have the following equation
[tex]f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})[/tex]
This gives
[tex]f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})[/tex]
Evaluate the products
[tex]f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})[/tex]
Evaluate the like terms
[tex]f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}[/tex]
So, we have
f(x) = x²+ 2/3x - 1/9
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multiplicative inverse of 7^-2
Answer:
[tex] 7^2[/tex]
Step-by-step explanation:
multiplicative inverse of[tex] \:\:7^{-2} =7^2[/tex]Answer:
7²
Step-by-step explanation:
the product of a number and its multiplicative inverse is equal to 1 , that is
a ×[tex]\frac{1}{a}[/tex] = 1
given
[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and
[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1
Which linear inequality is represented by the graph?1. y>2/3x-22. y<2/3x+23. y
To identify the inequality of the given graph:
1. Identify the equation of the borderline in slope-intercept form (y=mx+b)
- Find the slope (m): Use two points in the line in the next formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ Points\colon(-3,-3)and(3,1) \\ \\ m=\frac{1-(-3)}{3-(-3)}=\frac{1+3}{3+3}=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)
b= -1
Equation of the border line:
[tex]y=\frac{2}{3}x-1[/tex]2, Identifify the inequality sing:
-When the inequality is < or > the borderline is a dotted line
-When the inequality is ≥ or ≤ the border line is a full line
-When the inequality is < or ≤ the shaded area is under the borderline
-When the inequality is > or ≥ the shaded are is over the borderline
In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:
[tex]y<\frac{2}{3}x-1[/tex]Which polynomial represents the difference below?2x^2 + 7x+6(3x^2 - x)O A. 2x^2 + 5x + 6B. 2x^2 + 4x + 6c. - x^2 + 6x + 6D. - x^2 + 8x+ 6
The given polynomials are as ,
[tex]\begin{gathered} 2x^2+7x+6\text{ and} \\ 3x^2-x \end{gathered}[/tex]We have to subtracrt these given polynomials,
[tex]\begin{gathered} =2x^2+7x+6-3x^2-(-x) \\ =2x^2+7x+6-3x^2+x \\ =-3x^2+2x^2+7x+x+6 \\ =-x^2+8x+6 \end{gathered}[/tex]Option D is correct.
study questions from digital text book page 2.03 : Picture's down below
Question #1 : What is m∠SVT?
Question #2: What is the m∡BEC?
Disclaimer!! these are not from a Test, Quiz, or Assignment. these are from a practice page and i wanted to know how do these questions for a Future assignment with questions like these. I am just informing you guys because i didn't know the guidelines until now and i will no longer put test questions up because I am now aware its not ok to do so. So This Is not from a Test, Quiz, or Assignment. Thank you
The angle measures in this problem are given as follows:
1. Angle SVT: 79º.
2. Angle BEC: 65º.
Angle SVTAngles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:
8y - 33 = 5y + 9
3y = 42
y = 42/3
y = 14.
Hence the measure of the angle SVT is of:
m<SVT = 5y + 9 = 5(14) + 9 = 79º.
Angle BECThe two angles given in this problem are also vertical, meaning that we can solve for x as follows:
5x - 10 = 3x + 40
2x = 50
x = 50/2
x = 25º.
Then the bottom angle is:
3 x 25 + 40 = 115º.
The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:
115 + m<BEC = 180
m<BEC = 180 - 115
m<BEC = 65º.
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